Donald Yau: Operads of Wiring Diagrams

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Cover: 9783319950006 | Operads of Wiring Diagrams | Donald Yau | Taschenbuch | Paperback | xi

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Sprache: Englisch

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Beschreibung

Wiring diagrams form a kind of graphical language that describes operations or processes with multiple inputs and outputs, and shows how such operations are wired together to form a larger and more complex operation. This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads.The book proves finite presentation theorems for operads of wiring diagrams as well as their algebras. These theorems describe the operad in terms of just a few operadic generators and a small number of generating relations. The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra. A partial verification of David Spivak¿s conjecture regarding the quotient-freeness of therelational algebra is also provided. In the final part, the author constructs operad maps between the various operads of wiring diagrams and identifies their images.

Assuming only basic knowledge of algebra, combinatorics, and set theory, this book is aimed at advanced undergraduate and graduate students as well as researchers working in operad theory and its applications. Numerous illustrations, examples, and practice exercises are included, making this a self-contained volume suitable for self-study.

Über den Autor

Donald Yau is Professor of Mathematics at The Ohio State University at Newark. He obtained his PhD at MIT and held a post-doctoral position at the University of Illinois at Urbana-Champaign. His research focuses on algebraic topology. He has so far authored five books and over 30 articles.

Zusammenfassung

Provides a self-contained introduction to wiring diagrams, operads, and operad algebras

Includes over 100 illustrations and a chapter of practice problems

Presents generators and relations for both the operads and algebras of wiring diagrams introduced by David Spivak

Inhaltsverzeichnis

Introduction.- Part I Wiring Diagrams.- Wiring Diagrams.- Generators and Relations.- Decomposition of Wiring Diagrams.- Finite Presentation.- Finite Presentation for Algebras over Wiring Diagrams.- Part II Undirected Wiring Diagrams.- Undirected Wiring Diagrams.- Generators and Relations.- Decomposition of Undirected Wiring Diagrams.- Finite Presentation for Undirected Wiring Diagrams.- Algebras of Undirected Wiring Diagrams.- Part III Maps Between Operads of Wiring Diagrams.- A Map from Normal to Undirected Wiring Diagrams.- A Map from Wiring Diagrams to Undirected Wiring Diagrams.- Problems.

Details

Erscheinungsjahr:	2018
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	320
Reihe:	Lecture Notes in Mathematics
Inhalt:	xi 308 S. 437 s/w Illustr. 308 p. 437 illus.
ISBN-13:	9783319950006
ISBN-10:	3319950002
Sprache:	Englisch
Herstellernummer:	978-3-319-95000-6
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Yau, Donald
Auflage:	1st ed. 2018
Hersteller:	Springer International Publishing Lecture Notes in Mathematics
Maße:	235 x 155 x 18 mm
Von/Mit:	Donald Yau
Erscheinungsdatum:	20.09.2018
Gewicht:	0,487 kg

preigu-id: 113853574